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On Fri, Aug 05, 2011 at 01:12:28PM +0200, Gavin Wraith wrote:
> The trouble is, addition and multiplication cannot be commutative 
> ( x + y == y + x) or associative ( x + ( y + z ) == ( x + y ) + z ) 
> for floating point numbers. 

We're straying off-topic, but I can't let this pass.  Addition and
multiplication _are_ commutative.  Granted, if you have three numbers,
order of addition becomes important, but that is a consequence of 
non-associativity.  You have three possible answers, depending only 
on which of the three numbers sits out in the first addition.